arXiv subjects

Joel A. Middleton

Publications and source records attributed to Joel A. Middleton.

4 recordsLinked to original sources

arXiv2026

Optimized variance estimation under interference and complex experimental designs

Unbiased and consistent variance estimators generally do not exist for design-based treatment effect estimators because experimenters never observe more than one potential outcome for any unit. The problem is exacerbated by interference and complex experimental designs. Experimenters must accept conservative variance estimators in these settings, but they can strive to minimize the conservativeness. In this paper, we show that the task of constructing a minimally conservative variance estimator can be interpreted as an optimization problem that aims to find the lowest estimable upper bound of the true variance given the experimenter's risk preferences and knowledge of the potential outcomes. We characterize the set of admissible bounds in the class of quadratic forms, and we demonstrate that the optimization problem is a convex program for many natural objectives. The resulting variance estimators are guaranteed to be conservative regardless of whether the background knowledge used to construct the bound is correct, but the estimators are less conservative if the provided information is reasonably accurate. Numerical results show that the resulting variance estimators can be considerably less conservative than existing estimators, allowing experimenters to draw more informative inferences about treatment effects.

stat.ME↗

arXiv2021

Unifying Design-based Inference: On Bounding and Estimating the Variance of any Linear Estimator in any Experimental Design

This paper provides a design-based framework for variance (bound) estimation in experimental analysis. Results are applicable to virtually any combination of experimental design, linear estimator (e.g., difference-in-means, OLS, WLS) and variance bound, allowing for unified treatment and a basis for systematic study and comparison of designs using matrix spectral analysis. A proposed variance estimator reproduces Eicker-Huber-White (aka. "robust", "heteroskedastic consistent", "sandwich", "White", "Huber-White", "HC", etc.) standard errors and "cluster-robust" standard errors as special cases. While past work has shown algebraic equivalences between design-based and the so-called "robust" standard errors under some designs, this paper motivates them for a wide array of design-estimator-bound triplets. In so doing, it provides a clearer and more general motivation for variance estimators.

stat.ME↗

arXiv2021

Unifying Design-based Inference: A New Variance Estimation Principle

This paper presents two novel classes of variance estimators with superior properties, in the absence of parametric or semi-parametricassumptions. The first new class of estimator is the Oblozene Chlebizky (OC) variance estimators as a novel alternative to the generalized sandwich in Paper 1 of 4. That the OC concept is unlikely to arise from other, more standard, frameworks is manifestly true in light of the 40 year lacuna since White (1980). For any member of the generalized sandwich variance estimator class, there is an OC with the same expected value. The this alternative replaces a random matrix at the center with a nonrandom one. The second type of estimator is guaranteed conservative for the variance of the estimator and is based upon a similar principle of replacing a random matrix with its expectation.

stat.ME↗

arXiv2018

A Unified Theory of Regression Adjustment for Design-based Inference

Under the Neyman causal model, it is well-known that OLS with treatment-by-covariate interactions cannot harm asymptotic precision of estimated treatment effects in completely randomized experiments. But do such guarantees extend to experiments with more complex designs? This paper proposes a general framework for addressing this question and defines a class of generalized regression estimators that are applicable to experiments of any design. The class subsumes common estimators (e.g., OLS). Within that class, two novel estimators are proposed that are applicable to arbitrary designs and asymptotically optimal. The first is composed of three Horvitz-Thompson estimators. The second recursively applies the principle of generalized regression estimation to obtain regression-adjusted regression adjustment. Additionally, variance bounds are derived that are tighter than those existing in the literature for arbitrary designs. Finally, a simulation study illustrates the potential for MSE improvements.

math.ST↗